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Popular Word Problems >

If two fair dice are rolled, find the probability of a sum of 6 given that the roll is a ”double”

Solution

I f tw o f ai r d i ce a re ro ll e d, f in d t h e p ro babi l i t y o f a s u m o f 6 g i v e n t ha t t h e ro ll i s a ” d o u b l e ”

Solution

\frac{1}{6}

+1

Decimal

0.16666 \dots

Solution steps

The possible outcomes when two dice are rolled are

6 \cdot 6

Therefore, the number of possible outcomes:

6^{2}

Find the number of favorable outcomes of a sum of 6 given that the roll is a double:

6

Probability

= \frac{number of favorable outcomes}{total number of outcomes}

= \frac{6}{6 ^{2}}

Cancel the common factor:

6

= \frac{1}{6}

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